How can I make the section of a prolate ellipse like the one shown in the figure?
You could do it this way:

Create a cube, subdivide it 3 times and in the Operator box give it a Smoothness value of 1:



Cut the top half, scale on the Z axis:



Cut a hole:



Extrude all along the normals (AltE):



Create some edge loop, both to sharp the edge and to give it different colors:



Give it the colors, give it a Subdivision Surface modifier: